Consider the following equation: Yn (x) = by plotting the difference where n=0,1,.... and Ho(x) =1, and H(x) = 2x (a) Using python, make a plot of Un(x) for n = 0 and 1 on the same graph, in the range x = -8 to x = 8, with 200 points. (b) Using python, make a plot of the local kinetic energy - -n(x) on the same range. Use 'h' corresponding to the interval between the points from the above question (a). [See the note at the end for using 'h'] (c) Using python, verify that the following equation is properly satisfied at each point in the range, for each of these Un(x): 1 e 2"n! -x/2 H(x), [-2122 + 12x] #n(x) = En4u (x) dx An (x) = [-21/22 +22 - En] (x) 1 +=x dx df dx where E = 0.5 + n. Try smaller values of h to see how small you can get A, and comment on what limits the precision attainable. Note: For differentiation, use the following approximation: = f(x+h)-f(x - h) 2h